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 CMFD, 2013, Volume 49, Pages 99–131 (Mi cmfd248)

Compact subdifferentials in Banach spaces and their applications to variational functionals

I. V. Orlov, Z. I. Khalilova

Vernadskii Tavria National University, Simferopol, Ukraine

Abstract: We develop a theory of sublinear operators with compact values. Then, based on this theory, we construct a theory of first-order compact subdifferentials for maps in Banach spaces. The results are applicable to the calculation of compact subdifferentials of variational functionals with nonsmooth Lagrangians.

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English version:
Journal of Mathematical Sciences, 2015, 211:4, 542–578

UDC: 517.972+517.982.22

Citation: I. V. Orlov, Z. I. Khalilova, “Compact subdifferentials in Banach spaces and their applications to variational functionals”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 49, PFUR, M., 2013, 99–131; Journal of Mathematical Sciences, 211:4 (2015), 542–578

Citation in format AMSBIB
\Bibitem{OrlKha13} \by I.~V.~Orlov, Z.~I.~Khalilova \paper Compact subdifferentials in Banach spaces and their applications to variational functionals \inbook Proceedings of the Crimean autumn mathematical school-symposium \serial CMFD \yr 2013 \vol 49 \pages 99--131 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd248} \transl \jour Journal of Mathematical Sciences \yr 2015 \vol 211 \issue 4 \pages 542--578 \crossref{https://doi.org/10.1007/s10958-015-2617-9} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84946496291} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. Baran, I. Orlov, “Adjoint extremal problem for non-smooth functionals”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 23–26
2. I. V. Orlov, “Subdifferentials via sub-operators”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 235–238
3. F. S. Stonyakin, “Subdifferential calculus in abstract convex cones”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 316–319
4. F. S. Stonyakin, “Applications of subdifferential calculus to Bochner integral theory”, 2017 Constructive Nonsmooth Analysis and Related Topics, CNSA 2017, Dedicated to the Memory of V.F. Demyanov, ed. L. Polyakova, IEEE, 320–323
5. I. V. Orlov, “Introduction to sublinear analysis”, Journal of Mathematical Sciences, 218:4 (2016), 430–502
6. I. V. Orlov, I. V. Baran, “Introduction to sublinear analysis – 2: symmetric case”, Journal of Mathematical Sciences, 225:2 (2017), 265–321
7. I. V. Orlov, A. V. Tsygankova, “Multidimensional variational functionals with subsmooth integrands”, Eurasian Math. J., 6:3 (2015), 54–75
8. I. V. Orlov, “Inverse and Implicit Function Theorems in the Class of Subsmooth Maps”, Math. Notes, 99:4 (2016), 619–622
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